Mechanical energy (ENG) required by a time-varying elastance model of the ventricle was compared with oxygen consumption per beat (VO2) of the canine left ventricle contracting under a variety of loading conditions. ENG needed for this model to increase its elastance during systole is shown to be equal to the sum of the potential energy built in the elastance during systole plus the external mechanical stroke work. This ENG is equivalent to the area (PVA) bounded by the end-systolic and end-diastolic P-V curves and the systolic limb of the P-V loop trajectory in the P-V plane. There was a high correlation (r = 0.89) between VO2s documented in the literature and PVAs assessed by the author from the accompanying P-V data from both isovolumic and ejecting contractions in 11 hearts. A linear regression analysis yielded an empirical equation: VO2 (ml O2/beat) = a . PVA (mmHg . ml/beat) + b, where a = 1.37 X 10(-5) and b = 0.027, which can be used to predict VO2 from PVA. A preliminary experimental study in my laboratory confirmed the validity of this empirical equation.

Total mechanical energy of a ventricle model and cardiac oxygen consumption

Based on the recent data from the literature, we derived analytic expressions for ventricular stroke work (SW), ventricular O2 consumption, and the ratio of the former to the latter, defined as ventricular efficiency, in terms of ventricular contractile properties and arterial afterloading properties. The ventricular properties were quantified by Ees and V0, the slope and volume axis intercept, respectively, of the linear end-systolic pressure-volume relationship. Ventricular afterload was represented by the effective arterial elastance (Ea), a parameter that is dependent on aortic input impedance parameters. O2 consumption was assessed by estimating ventricular pressure-volume area, which has been shown to be linearly related to O2 consumption. Model analysis indicated that SW is maximum when Ea = Ees, the afterload that results in the greatest efficiency is always less than that which provides the maximum SW, the SW and efficiency of a weak heart are more sensitive to changes in afterload than in a strong heart, and there is a sigmoidal relation between ventricular efficiency and end-diastolic volume that reaches its maximum at volumes outside the upper limit of the physiological range. Further analysis of the model indicated that under physiological conditions ventricular and arterial properties may be adjusted more toward optimization of efficiency than SW.

Ventricular efficiency predicted by an analytical model.

We analyzed the effect of positive inotropic agents on the relation between left ventricular oxygen consumption and the systolic pressure-volume area. Pressure-volume area is a measure of total mechanical energy for ventricular contraction, and is a specific area in the ventricular pressure-volume diagram circumscribed by the end-systolic and end-diastolic pressure-volume relation curves and the systolic segment of the pressure-volume trajectory. Either epinephrine (1 microgram/kg per min, iv) or calcium ion (0.03 mEq/kg per min, iv) was administered to canine excised cross-circulated hearts. These agents increased an index of ventricular contractility, Emax, or the slope of the end-systolic pressure-volume line, by 70%. The regression lines of ventricular oxygen consumption on pressure-volume area in control and in enhanced contractile states were of the same formula: ventricular oxygen consumption (ml O2/beat per 100 g) equals A times pressure-volume area (mm Hg ml/beat per 100 g) plus a constant B. Coefficient A remained unchanged at 1.8 X 10(-5) ml oxygen/(mm Hg ml), but constant B increased from 0.03 ml oxygen/beat per 100 g by more than 50% with either agent. The reciprocal of A reflects the energy conversion efficiency for the total mechanical energy, and this efficiency remained near 36%. The increase in B was equal to the directly measured increment in ventricular oxygen consumption for mechanically unloaded contraction. The basal metabolism remained unchanged. We conclude that the augmented oxygen consumption under the acutely enhanced contractile state with either epinephrine or calcium was caused primarily by an increased energy utilization associated with the excitation-contraction coupling.

Effect of positive inotropic agents on the relation between oxygen consumption and systolic pressure volume area in canine left ventricle.

Neither stroke volume nor external cardiac work (the integral of pressure times flow during ejection) has been considered an important correlate of myocardial oxygen consumption. An initial set of experiments re-examined this question of independently varying heart rate, systolic blood pressure, and stroke volume in seven closed-chest, anesthetized dogs. This was achieved by cardiac pacing, a pressure control reservoir, phenylephrine infusion, and adjustment of arteriovenous shunts. Propranolol was used to minimize changes in contractility which might affect myocardial oxygen consumption. Stroke volume in the form of external work had a significant effect on oxygen consumption. From these results, a new pressure-work index of myocardial oxygen consumption was devised, and fitting parameters for the following indexes were determined: systolic pressure-rate product, estimated wall tension, external left ventricular work, triple product, mean pressure-rate product, Et (Bretschneider), and tension-time index. These indexes were prospectively applied to a second set of experiments in 11 closed-chest, anesthetized dogs given norepinephrine, isoproterenol, dobutamine, Nembutal, and propranolol to alter myocardial contractility. Inotropic oxygen wasting was observed with the tension-time, mean pressure-rate, triple product, and estimated wall tension indexes, but not with the pressure-work or systolic pressure-rate indexes. It is concluded that stroke work is an important correlate of myocardial oxygen consumption, and that the pressure-work of systolic pressure-rate indexes can account for catecholamine-induced, changes in myocardial oxygen consumption without postulating an oxygen-wasting effect.

Work as a correlate of canine left ventricular oxygen consumption, and the problem of catecholamine oxygen wasting.

The ventricular systolic pressure-volume area correlates well with myocardial oxygen consumption. However, in isolated muscle preparations, there are experimental data based on both mechanical and energetic measurements that suggest that the pressure-volume area concept may not obtain. In the present study, force-length area, the analog of pressure-volume area for a linear muscle, was examined in the ferret papillary muscle preparation under a wide range of loading conditions. There were two major findings: first, force-length area is closely correlated with oxygen consumption (r = 0.94-0.98); this correlation is better than those for such other indexes as peak force and force-time integral. Furthermore, this relation of oxygen consumption with force-length area is independent of the mode of contraction (isometric or shortening), while the relations with the other indexes are not. Second, quick release imposed after end-systole during isometric contraction was found to curtail oxygen consumption. The first finding, the optimal correlation of force-length area with oxygen consumption, suggests both that the correlation of pressure-volume area with oxygen consumption on the ventricular level arises from a basic property of cardiac muscle and that force-length area may be the best mechanical index to use in calculating regional oxygen consumption for a ventricular segment. The second finding, however, suggests that the time-varying elastance model, on which the concepts of pressure-volume area and force-length area are based, may not provide a complete description of the mechanical basis of cardiac muscle energetics, especially during the isometric contraction.

Correlation of force-length area with oxygen consumption in ferret papillary muscle.

The relationship between the force in the left ventricular wall during systole and myocardial O2 consumption (MVO2) was determined. In addition, the relative influence of the load imposed during shortening and fiber shortening on MVO2 was assessed. For this purpose, 14 servo-regulated, paced, isolated canine hearts were used and the steady-state response in total coronary flow and arteriovenous oxygen difference was measured. For both the isovolumetrically beating and the ejecting ventricle, statistically significant linear relations were observed between MVO2 and the integral of systolic force. These relations were not significantly different from one another, indicating that shortening was not a determinant of MVO2. Moreover, when ejecting an isolumetric beats of equivalent developed force were compared, a difference in MVO2 (deltaMVO2) was found. deltaMVO2 was a function of the force integral difference between these contractions and not fiber shortening. Thus, under the conditions of this experiment, the integral of systolic force that includes developed force and shortening load is the predominant factor regulating MVO2 for any given contractile state, whereas the influence of fiber shortening is negligible.

Myocardial oxygen consumption: the role of wall force and shortening

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Myocardial oxygen consumption: the role of wall force and shortening